A Novel Approach for Stock Price Modeling based on Fractional Integration Analysis

Abstract

This paper deals with the modelling of stock market prices using a novel flexible I(d) technique for time series analysis. We employ both fractional integration and structural break techniques in studying the monthly share price structure of the Nigerian stock market. Our data span between 1987 and 2017. The results obtained using both parametric and semiparametric methods indicate little evidence of mean reversion since most of the orders of integration are equal to or higher than 1. The possibility of structural breaks is also taken into account and the results indicate the existence of two break dates: one at 1996m1 and the other one at 2005m1. Imposing a white noise process for the d-differenced processes, we notice that the time trend is only required for the first subsample, where the estimated value of d is equal to 0.85, and the unit root null hypothesis cannot be rejected. For the remaining two periods, an intercept seems to be sufficient and the I(1) hypothesis is rejected in favour of d > 1. Very similar results are obtained under autocorrelated disturbances, the corresponding values of d being 0.93, 1.32 and 1.20 respectively for the first, second and the third subsamples.